Macy’s, the department store chain, reported a 6.2 percent gain, and the luxury retailer Nordstrom posted an 8.7 percent increase in revenues for the month.

Across the country, chain store sales were up 3.5 percent in December after two months of lackluster reports, according to the International Council of Shopping Centers. But sales for the holiday season - November and December - rose just 3.3 percent, below analysts’ projections and less than the 3.8 percent gain in 2010. This two-month stretch is a critical period when merchants typically generate up to 40 percent of their annual revenue.

“American consumer demand is sluggish and fickle; most retailers had to depend on deep price discounts in order to increase sales revenue, taking a bath on per unit profits - sales up, margins down,’’ said Chris G. Christopher Jr., a senior principal economist at IHS Global Insight in Lexington.

“When there is a fight for market share in a soft economy there will be winners and losers. There are too many retailers chasing after frugal and fatigued shoppers.’’

Merchants faced several challenges during the holiday season, including rising prices for cotton and other commodities and unseasonably warm weather that discouraged shoppers from buying jackets, sweaters, and other winter goods. That left retailers holding large inventories into late December and triggered major discounting at chains such as J.C. Penney and Kohl’s, said Michael P. Niemira, chief economist at the International Council of Shopping Centers in New York.

Kohl’s Corp. reported that revenue at stores open at least a year, known as same-store sales, dropped 0.1 percent in December after tumbling 6.2 percent in November, a result that was far weaker than what analysts had expected.

TJX’s chief executive, Carol Meyrowitz, said in a statement yesterday that the 8 percent sales increase exceeded the company’s expectations, but she acknowledged it relied on low prices throughout the season to motivate consumers.

“We made a strategic decision to price aggressively in order to reinforce our value position in a very promotional retail environment, and to clear cold weather apparel in this unseasonably warm winter,’’ Meyrowitz said.

The last two months marked the most intense discounting in a decade - excluding the desperation sales during the 2008 economic meltdown - said Ken Perkins, president of Retail Metrics Inc. in Swamspcott.

The 2011 promotions resulted in great deals for consumers and more robust top lines for merchants, but “this did, however, come at a cost to retailers’ bottom lines,’’ Perkins said. “Margins were under pressure from stepped up discounting, free shipping, price matching, greater expenses for increased advertising, and expanded store hours.’’

Retail analysts are projecting a similarly challenging environment in 2012, with the gulf between weak and strong merchants growing wider.

“American households are looking at a weak labor market, high debt burdens, house prices that have not yet hit bottom, price increases that have outpaced wage growth, and a lack of confidence in the government’s ability to make things better,’’ Christopher, of IHS Global Insight, wrote in his report yesterday.

“Recent consumer spending has been supported by a declining saving rate, not a solid foundation for retail sales growth. Retailers will have to adapt or suffer the consequences.’’

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